This source form $\mathbf{E}$ is the Euler-Lagrange form of $\mathbf{L}$. It vanishes precisely at those points which are solutions to the Euler-Lagrange equations induced by $\mathbf{L}$.

The combination $\rho \coloneqq \mathbf{L} + \theta$ is the corresponding Lepage form.

References

G. J. Zuckerman, Action principles and global geometry , in Mathematical Aspects of String Theory, S. T. Yau (Ed.), World Scientific, Singapore, 1987, pp. 259€284. (pdf)

Last revised on November 8, 2017 at 15:17:59.
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